Sunday, September 30, 2018

Puddle Play - Rethinking the 'Math Classroom'

We are always looking for opportunities to head outside and enjoy the weather, even when it might be a little wet or cold. Last week our area enjoyed quite a bit of heavy autumn rain. The children spent much of the morning peering through the window and marveling at how much rain was falling. After a few hours they noticed a giant puddle forming in the corner. As the rain continued to fall and the puddle grew, the children became concerned that their outdoor play time would be hampered by the rain.

Fortunately by the early afternoon the rain tapered and the children were able to head outdoors. We are lucky to have a class set of rain boots purchased by the school parent council for use in our outdoor classroom. This way children can enjoy playing in our school yard, even when they might forget to bring their boots to school that day. We are always prepared and the children ready to explore the world outdoors. Even the giant puddle would be no problem that day!

The children scurried outside after eating lunch - many wearing mismatched school boots because they couldn't get them on their feet fast enough because they were so eager to explore the water.


As I approached them I was amazed by the authentic math talk developing in this natural and authentic learning environment. As I listened into their conversations I overhead children wondering with each other about amazingly big math ideas...

How many children could fit in the puddle?  Did each person's feet have to be touching to be counted? Did children who were jumping in and out of the puddle count too?

How deep was the water? How much water was there really in the big puddle? Could it fill a bath tub? How could it even be measured?

Who could make the biggest splash? How would they even judge how big the splash was? Could it be measured? Was the biggest splash the one that soaked the most children standing nearby?

Could the water be used to make soup? How much water was needed in the recipe? Would anyone even want to eat mud soup?

How much water was in one's rain boots after a big splash? How long did it take to dump it out? How did all that water get in there in the first place?

How much more water was needed to cover the stump? Was the stump floating or sinking in the water?  How tall was the stump? What if it rained more...would the stump be under water?

How long would it take to run across the puddle? Who could run the fastest over the water? How could we measure and record the puddle races?

The children were making connections between their puddle play and math in the world around them. The questions they were posing about their experiences in the water were meaningful to them, supporting and strengthening their productive disposition towards math. As an educator involved in their play, I was able to listen to their questions and facilitate conversation and critical thinking about the big math ideas. How could we figure out who could make the biggest splash? What experiences did the children have measuring the size of something irregular. What tools and resources were available to help support this inquiry? Could technology play a role? Would children be interested in revisiting these math questions at a later time or would their interest only occur when playing in the puddles?

As the children and I engaged in conversations about their questions they were developing adaptive reasoning skills - this is the capacity for logical thought, reflection and justification in their math thinking. As children connected what they were observing and experiencing in the puddle play to their own unique experiences and ideas, they were engaged in rich learning as they reflected upon and justified their questions, ideas and strategies to solve the puddle math problems.

Even though many of the children's questions were not answered, the purposeful outdoor math exploration encouraged children to develop a strong conceptual understanding of a variety of developmentally appropriate math topics related specifically to our curriculum including measurement, counting, capacity, classification, time and quantity. I was able to support their conversations and provide suggestions and strategies in the moment. I became a play participant together with them by playing in the puddles myself.

What had originally looked to be a damper on our outdoor fun turned into a complex and layered opportunity for rich math thinking during an activity that most children love to do - explore the rain. It just shows that math can happen anywhere, anytime, when we are willing to rethink what the 'math classroom' should look like.

Sunday, September 16, 2018

Anchor of Five

Anchor of 5

A successful math program for children will have an emphasis on number sense as its foundation. Number sense is a natural part of all other strands (e.g., geometry, patterning, data management). Exploring number relationships help children build fluency, accuracy and confidence. Five frames provide a visual reference to the anchor of 5. Five is a 'friendly number' for children. They associate five with the most natural of math 'manipulatives' that they always have available...fingers on one hand! The number system that we use in Canada encourages an understanding of place value that is dependent on groupings of 10, and understanding groups of 5 will evolve into 10. This is a key foundation for future place value work. Here is a review of some of our math work this week. 
Read alouds
We used many engaging, patterned texts during our whole group circle time that focused on groups of 5. In books like 'Five Busy Beavers' a group of 5 beavers slowly decreases to 1 as each beaver leaves the water for other adventures. Children can see the group decrease by 1 each time, and predict what the new number will be. They can subitize the new number as they observe the number of beavers on each page, or follow along and use their fingers to chant along with the text. This book can then be added to a math centre where manipulatives can be provided to further enhance the text and encourage children to play with the numbers 1 through 5.
A Number Station
During free choice time the children had the opportunity to visit a math centre where various manipulatives and tools were made available for children to play with the numbers. A number line, wooden and mirror numbers, five frames, finger tracers, and natural materials were available for children to explore. Students matched, counted, sorted, patterned, and ordered the manipulatives, often composing groups of 5.
Morning Message
Each morning we start our day with a morning message. One of the most important words that children first learn to read and write are their names (their own, and those of their peers). We used our 'star of the day' to model how our names fit into five frames (and sometimes beyond the five frame if the name has more than five letters). This helped us conceptualize the anchor of five and also introduced some concepts of print too (e.g., that words are composed of letters and that letters represent sounds).
Number Line
We brought a number line outdoors with us during our outdoor play time. It was interesting to see how the children created their own games without adult prompting. Some children gathered natural materials and placed them next to the numbers (e.g., 7 stones next to the number 7). Others used the line as a tool in a jumping game, starting at the 0 and seeing who could jump the furthest and reach the biggest number!
How Many are Hiding?
Whole group time is also a great opportunity to introduce meaningful math games that children can then play in small groups or during free choice play time. To help children compose to the anchor of five, we used a group of five unifix cubes. Children are first shown the five in a line. The player then hides some cubes behind his/her back and shows the group the remaining cubes. The group has to calculate how many cubes are hidden, encouraging them to subitize and compose to the anchor of 5. They indicate the missing quantity by holding their fingers up to the player who then reveals the missing quantity.


We love to sing each day. Our children loved the fingerplay "Five Little Monkeys Swinging in a Tree". To enrich the experience with meaningful math, we added a magnetic five frame to the song. As the children sang along and used their fingers to decompose the number 5 to 1, we removed counters from the frame as they count. During play time many children enjoyed leading their peers in a singing of the song!

Pentomino Challenge
Pentominoes are a wonderful math manipulative that encourage spatial reasoning and use an anchor of five as each unique piece is created using five small squares. A challenge that encouraged perseverance and spatial logic this week involved challenging the children to fill a standard cookie tray with pieces, leaving no gaps in the puzzle. 

We love learning from others! Share your favourite math activities that encourage an exploration of the anchor of 5 in the comments below!
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